Digital binary MEMS wavefront control

ABSTRACT

A phase screen, i.e., an opto-electronic device that can convert a distorted incoming optical wavefront into a plane wave or, conversely, transform a plane wave into a prescribed varying output wavefront. Binary all-digital MEMS interferometer configurations that can be used to create controlled and arbitrary optical wavefront using only 0,1 amplitude changes followed by differential propagation distances to convert these amplitude variations into controllable and/or continuous phase variations. Clustered pixel notions, such as Floyd-Steinberg, Stucki or other algorithms useful in digital half-tone printing, are simultaneously employed to create controllable grey-level variations as well as continuous phase variations. Desired grey-levels can be obtained wherein each pixel is formed by, e.g., a 3×3 or 5×5 cluster of mirrors. Both the filling-in of the outputs of the binary mirror (0,1) and the grey-levels are accomplished simply by spatial averaging over a short propagation distance.

RELATED APPLICATIONS

This application is a continuation of, and claims the full line ofpriority to U.S. application Ser. No. 12/304,025 filed on Dec. 9, 2008,which itself is a US national stage filing of PCT/US2006/025254 filed on28 Jun. 2006, the subject matter of which are incorporated herein byreference in their entireties.

FEDERALLY SPONSORED RESEARCH

This invention was made with U.S. Government Support under ContractNumber DAAD 19-03-1-0185 (44430-PH), awarded by the US Army ResearchOffice. The Federal Government has certain rights in the invention.

BACKGROUND OF THE INVENTION

1. Field of the Invention

Embodiments of the invention are most generally related to the field ofoptical modulation and opto-electronic imaging. More particularly,embodiments of the invention are directed to novel apparatus and methodsthat effect phase and absolute value of the amplitude, hereinafteramplitude, control over an optical wavefront, and to applicationsdirected to atmospheric sensing, optical metrology, astronomical andophthalmic imaging, adaptive optics and interferometry.

2. Description of Related Art

In optical interferometry one often needs to generate a particularfunction form for the variation of amplitude over a given transverseplane starting, for example, from a uniform plane wave. As a specificinstance in optical metrology, one generates the family of Zernikepolynomials using modern optical interferometers with special masksincorporated. These specified wavefronts are used to test the accuracyof a particular optical surface being fabricated. In addition there areother instances when a distorted wavefront needs to be corrected so asto provide a plane wave output or a converging wave of specific radiusof curvature for the equiphase of the propagating wave. For instance,when an optical signal travels from point A to point B, the quality ofthe received signal is less than that of the transmitted signal. Thisdegradation is due to variation in the uniformity of the medium (indexof refraction) that the light propagates through in going from point Ato point B. Common examples include the light from a star that isdistorted by atmospheric turbulence; poor vision due to defects in theoptics of the eye; and, noisy communication caused by a non-uniformindex of refraction over the signal path.

Viewed simply, a point source of light such as a star, for example,radiates spherical wavefronts of light in all directions. A wavefront isthe locus of points having the same phase i.e., have the same pathlength from the source. To a distant viewer on earth, the wavefront ofthe light traveling along the viewer's line of sight is in the form of aflat, uniform plane of light; i.e., a plane wavefront. However, when theindex of refraction of the propagation medium changes, the path lengthsare no longer equal or normal to the propagating plane wavefront.Instead, the wavefront is distorted or aberrated. Thus the phase of thewavefront is no longer uniform over the spatial extent of the wavefront.

Wavefront sensors are now commonly used to measure higher-orderaberrations of a wavefront propagated through an optical system. AShack-Hartmann sensor is often the principal component of modernophthalmic wavefront measuring devices. Several other types of wavefrontsensors are also commercially popular. Once a distorted wavefront ismeasured and quantified, it may be desirable to compensate thewavefront; i.e., to bring it back to its non-aberrated state. Deformablemirrors, referred to as adaptive or active optics (AO) depending upontheir application, are well known in the art. An adaptive optics imagingsystem, for example, is designed to correct for phase distortions in theoptical wavefront in near real time to obtain improved image quality.Adaptive optical imaging originated as a tool for improving theperformance of ground-based large telescopes for astronomical imagingthrough atmospheric turbulence. Another application is the correction ofatmospheric turbulence over horizontal propagation paths. Adaptiveimaging techniques have also been applied to wavefront control of largeastronomical telescopes by using high power lasers and guide stars togenerate perturbed wavefronts for correction of the astronomical image.Adaptive optics and wavefront control are also commonly used in laserfusion to correct for minute phase perturbations as the laser beampropagates through various lenses of the system. The typical componentsused in a present day adaptive system are listed in Table 1.

TABLE 1 Wavefront Sensors Wavefront Correctors Shack-Hartmann SensorContinuous membrane mirrors with PZT Curvature sensor Segmented mirrorswith PZT Shearing interferometer Bimorph Mirrors Smartt interferometerMEM micro-mirrors Pyramid sensor Liquid Crystal SLMsConventional designs for wavefront correctors include segmented mirrordevices with each mirror segment having tip/tilt and piston controls,and continuous membrane (analog) devices with a number of actuators ontheir back side for deforming the mirror surface. Bimorph mirrortechnology uses two piezoelectric wafers bonded together with an arrayof electrodes. The outer surface of one of the mirror acts as a mirror.These devices are most suitably used with a curvature sensorconfiguration. More recent technologies used for phase screens, as theyare sometimes called, include liquid crystal spatial light modulators(SLMs) and analog-type MEMS based micro-mirrors. Spatial lightmodulation is used, for example, in the fields of optical informationprocessing, projection displays, video and graphics monitors,televisions, astronomy and electrophotographic printing. There, opticalbeams are deflected by mirror arrays where it is desired to be able toindividually phase adjust the reflected light from each mirror. Often,the phase screen in an AO telescope is the single most troublesomecomponent in the system. Typically, the phase screen is an LCD used intransmission mode with a voltage applied in an x-y coordinate system,pixel by pixel. It can also take the form of multiple PZT actuators usedto push or deform a smooth mirror membrane into an aberrationcompensating surface shape.

Cost is an important factor in choosing an appropriate deformable mirrortechnology for a given application. Piezo-activated (PZT) deformablemirrors can cost over $1000 per actuator, thus a large mirror array canbe extremely expensive. MEMS devices are typically manufactured usingfabrication methods developed in the semiconductor industry.Comparatively, MEMS technology offers a low-cost attractive alternative.There are generally two types of micro-mirror arrays: (1) Devices withpiston and tip/tilt controls for micro-mirrors; and (2) simple ON/OFFtype binary micro-mirror arrays. The state-of-the-art devices of thefirst type have ˜1000 micro-mirrors each about 300 microns on a side,and each having an ˜2 micron piston stroke motion and ˜7 kHz frame rate.The ON/OFF type (i.e., digital binary MEMS) devices on the other handhave close to a million mirror elements, each being ˜17 micron on aside. Digital binary MEMS mirror technology has been developed over thelast two decades. Arrays consisting of ˜10⁶ mirrors that impart binary(1,0) amplitude modulation to the incident wavefront at ˜10 kHz framerates are now available commercially at low cost. They have foundwidespread application, for example, in projection display systems. Inrecent years other applications of these arrays have evolved, e.g. ingeneration of (1,0) mask patterns in lithography, for implementing amoving aperture in a confocal microscope, for obtaining multiplexingHadamard type mask patterns in spectroscopy applications, etc. Theability to provide only (1,0) type amplitude modulation has thus farbeen treated as a limitation that has prevented their use in adaptivesystems for phase correction. A new way of wavefront phase coding isrequired that will permit the use of binary mirror arrays for wavefrontphase modulation.

It is possible to generate selected wavefronts using deformable MEMSmirrors or LCD spatial light modulators. There are, however, certaindisadvantages associated with their use. These devices typically cannotwork over a broad range of wavelengths from the visible to longwavelength infra-red. As mentioned above, the cost for a 1000×1000actuator assembly is prohibitive. MEMS devices currently used inadaptive optics setups do not offer as high resolution as may be desiredfor a particular application. The control of a large mirror array iscomplex and a large MEMS array can be susceptible to backlash errors.Half-toned characterization of phase front, as will be described belowand used in conjunction with embodiments of the instant invention, wouldrequire high computational loading using the aforementioned deformablemirror devices.

In view of the challenges and disadvantages associated with wavefrontphase control using deformable mirrors and/or LCD SLMs, the inventorshave recognized that significant benefits may be realized by the variousembodiments and aspects of the invention described in detail below andas defined in the appended claims. As mentioned above, a new way ofwavefront phase coding is required that will permit the use of digitalbinary mirror arrays for wavefront phase modulation. The ability togenerate an arbitrary wavefront using only binary (ON/OFF) micro-mirrorarrays combined with digital half-toning methods and differentialpropagation distances has several advantages over deformable analog MEMSmirrors or LCD spatial light modulators. The benefits and advantagesinclude, but are not limited to, the ability to generate arbitrarywavefronts using only binary (ON/OFF) micro-mirror arrays combined withdigital half-toning methods; broadband performance over the wavelengthrange from the visible to LWIR; an effective frame size of ˜200×200 to300×300 pixels using digital half-toning algorithms over, e.g., 3×3 or5×5 mirror blocks at a fraction of the cost for comparable MEMSperformance; resolution that far exceeds analog MEMS device capability;simpler operation; less susceptibility to backlash errors; lowercomputational load, easy system calibration; all digital architecture;environmental robustness and stability, and others that will berecognized by persons skilled in the art.

As used herein, the term ‘analog’ refers to a continuous membrane mirrorsurface that may be deformed by a number of actuators coupled to therear surface of the membrane, or, to a MEMS device where the individualmirrors can be stepped over multiple positions instead of simple binary0,1. In contrast, a ‘digital’ binary MEMS mirror, as that term will beused in conjunction with various embodiments and aspects of theinvention described herein, will refer to a MEMS mirror array in whicheach individual mirror segment can only be in an “ON” position (referredherein below as having a 1 value and oriented to retro-reflect incidentlight) or an “OFF” position (referred to herein below as having a 0value and tilt-oriented to reflect incident light away from the intendedoptical path).

FIG. 1 shows what is known as an Argand diagram, which is used toillustrate the geometric representation of a complex number as simply apoint in the complex plane. An Argand diagram is a plot of complexnumbers as points z=x+iy in the complex plane using the x-axis as thereal axis and the y-axis as the imaginary axis, where z=(abs)z e^(iθ).In the figure, the radius of dashed circle represents the complexmodulus (abs)z of z and the angle θ represents its complex argument orwhat can be called the phase. The phase, θ, corresponds to thecounterclockwise angle from the positive real axis, i.e., the value of θsuch that x=(abs)z (cos θ) and y=(abs)z (sin θ). Since a wavefront maybe described by Euler's equation e^(i θ(x,y))=cos θ+i sin θ, inconjunction with various embodiments of the invention described hereinbelow, the notation of the Argand diagram may be useful to the reader inillustrating various aspects of the invention.

The advantages and benefits provided by the teachings disclosed hereinand the embodiments of the invention disclosed and claimed will becomemore apparent to persons skilled in the art in view of the followingdescription and drawings.

SUMMARY OF THE INVENTION

Most generally, embodiments of the invention are directed to a new typeof phase screen, i.e., an opto-electronic device that can convert adistorted incoming optical wavefront into a plane wave or, conversely,transform a plane wave into a prescribed varying output wavefront. Thebasic concept involves novel binary all-digital MEMS configurations thatcan be used to create an arbitrary optical wavefront using only 0,1amplitude changes followed by differential propagation distances toconvert these amplitude variations into controllable and/or continuousphase variations. As used herein, the term ‘arbitrary’ wavefront refersto a pixel phase value that can be represented anywhere in the complexplane described by an associated Argand diagram, rather than just on theunit value circle boundary or on some other restricted portion of thecomplex plane. Clustered pixel notions, such as Floyd-Steinberg, Stuckior other algorithms useful in digital half-tone printing, aresimultaneously employed to create controllable grey-level variations aswell as continuous phase variations. Desired grey-levels can be obtainedwherein each pixel is formed by a cluster of 3×3 mirrors or 5×5 mirrors,for example. Both the filling-in of the outputs of the binary mirror(0,1) and the grey-levels are accomplished simply by short propagation.

According to an embodiment of the invention, an optical controlcomponent includes a first component beam divider/combiner disposedalong a first component input optical path of an incident opticalwavefront; a first component binary MEMS device M1 ₁ comprising an(n_(x,y)×m_(x,y))_(M1) mirror array disposed optically downstream of thefirst component beam divider/combiner along an M1 optical path having atotal optical path length L1 ₁ (i.e., L1 is a double-pass distance); afirst component binary MEMS device M2 ₁ comprising an(n_(x,y)×m_(x,y))_(M2) mirror array disposed optically downstream of thefirst component beam divider/combiner along an M2 ₁ optical pathdifferent than the M1 ₁ optical path having a total optical path lengthL2 ₁; and phase retarder means for making L1 ₁ different than L2 ₁,wherein at least an M1 ₁ mirror sub array (X×Y)_(M1) is in an ON/OFFstate and a complementary at least an M2 ₁ mirror sub array (X×Y)_(M2)is in an OFF/ON state, further wherein an output wavefront propagatingalong a first component output optical wavefront path has a controlledmodulation.

Another embodiment of the invention is directed to an optical controldevice comprising a first optical control component as describedimmediately above; a second optical control component including a secondcomponent beam divider/combiner disposed along a second component inputoptical path of an input optical wavefront; a second component binaryMEMS device M1 ₂ comprising an (n_(x,y), m_(x,y))_(M1) mirror arraydisposed optically downstream of the second beam divider/combinercomponent along an M1 ₂ optical path having a total optical path lengthL1 ₂; a second component binary MEMS device M2 ₂ comprising an (n_(x,y),m_(x,y))_(M2) mirror array disposed optically downstream of the secondbeam divider/combiner component along an M2 ₂ optical path differentthan the M1 ₂ optical path having a total optical path length L2 ₂; andphase retarder means for making L1 ₂ different than L2 ₂, wherein atleast an M1 ₂ mirror sub array (X×Y)_(M1) is in an ON/OFF state and acomplementary at least an M2 ₂ mirror sub array (X×Y)_(M2) is in anOFF/ON state, further wherein an output wavefront propagating along asecond component output optical wavefront path has a controlledmodulation; an input beam divider disposed optically intermediate anincoming wavefront and the first and second optical control components,wherein the output optical wavefront from the input beam divider is theinput optical wavefront to the first and second optical controlcomponents; an output beam combiner disposed to optically combine therespective first and second component modulated output wavefronts; andphase shifting means for providing a controlled phase difference betweenthe first and second component phase modulated output wavefronts,wherein a resultant output wavefront has a phase that is different thanthe input optical wavefront phase by an amount θ(x,y).

An alternative embodiment of the invention is directed to an opticalcontrol device that uses a two-level half-toning algorithm to generate acontrolled wavefront. The device comprises a diffractive, inputwavefront divider/combiner (G) disposed along an optical axis of theinput wavefront; a first component diffractive wavefrontdivider/combiner (G1) disposed to optically intercept one of a positiveand a negative n^(th)-order output beam from the input wavefrontdivider/combiner; a first component binary MEMS device M1 comprising an(n_(x,y), m_(x,y))_(M1) mirror array disposed optically downstream ofthe first beam divider/combiner component along an M1 optical path,wherein at least an M1 mirror sub array (X×Y)_(M1) is in a selectedON/OFF state that provides a half-tone phase value H, where 0≦H≦1; asecond component diffractive wavefront divider/combiner (G2) disposed tooptically intercept either a complementary negative or positiven^(th)-order output beam from the input wavefront divider/combiner; asecond component binary MEMS device M2 comprising an (n_(x,y),m_(x,y))_(M2) mirror array disposed optically downstream of the secondbeam divider/combiner component along an M2 optical path, wherein acomplementary M2 mirror sub array (X×Y)_(M2) is in a selectedcomplementary OFF/ON state that provides a half-tone phase value (1−H),where 0≦(1−H)≦1; and at least one optical component that in-couples theinput wavefront and out-couples an output wavefront having a controlledphase that is different than the input wavefront phase. According to anaspect, the diffractive wavefront divider/combiner, the first componentdiffractive wavefront divider/combiner and the second componentdiffractive wavefront divider/combiner are diffraction gratings eachhaving a grating period Λ.

Another embodiment of the invention is directed to an optical controldevice comprising a polarizing beam divider/combiner disposed along acomponent input optical path of an incident optical wavefront, providingone polarization state P1 ₁ and another polarization state P2 ₁; aquarter wave plate which on two passes will cause the exiting P1 torotate by 90 degrees so as to pass through the polarizer beamdivider/combiner; a first binary MEMS device M1 ₁ comprising an(n_(x,y), m_(x,y))_(M1) mirror array disposed optically downstream ofthe polarizing beam divider/combiner along an M1 ₁ optical path of P1,wherein at least an M1 mirror sub array (X×Y)_(M1) is in a selectedON/OFF state that provides a half-tone phase value (1−H), where0≦(1−H)≦1; a second quarter wave plate; and a second binary MEMS deviceM2 comprising an (n_(x,y), m_(x,y))_(M2) mirror array disposed opticallydownstream of the polarizing beam divider/combiner along an M2 opticalpath of P2, wherein an M2 mirror sub array (X×Y)_(M2) is in a selectedcomplementary OFF/ON state that provides a half-tone phase value H,where 0≦H≦1, further wherein an output wavefront propagating along anoutput optical wavefront path has a polarization coded phase profileover a transverse cross section of the output wavefront.

According to a related embodiment, a grating-based interferometer deviceuses a novel three-level half-toning algorithm to generate an arbitrarywavefront having controlled amplitude and phase. In this embodiment, athird MEMS component is disposed so as to intercept the zero-orderdiffracted beam. The wavefront can be expressed as the sum ofpolynomials in H(x,y) having appropriate phase. When relative phasedelays are introduced between each of the three beams, they can becombined to produce an arbitrary wavefront having an absolute amplitudeand phase expressed as a(x,y) exp[iθ(x,y)].

Another embodiment of the invention is directed to an optical controldevice, comprising a beam divider/combiner disposed along an inputoptical path of an incident optical wavefront; a first binary MEMSdevice M1 comprising an (n_(x,y), m_(x,y))_(M1) mirror array disposedoptically downstream of the first component beam divider/combiner alongan M1 optical path providing an M1 _(out) wavefront, wherein at least anM1 mirror sub array (X×Y)_(M1) is in an ON/OFF state that provides ahalf-tone phase value expressed as 1−H(x,y), wherein H(x,y) represents atwo-level value equal to 0 or 1; a second binary MEMS device M2comprising an (n_(x,y), m_(x,y))_(M2) mirror array disposed opticallydownstream of the beam divider/combiner along an M2 optical pathproviding an M2 _(out) wavefront, wherein a complementary M2 mirror subarray (X×Y)_(M2) is in an OFF/ON state that provides a half-tone phasevalue expressed as H(x,y); and phase retarder means for providing acontrolled phase difference between the M1 _(out) wavefront and the M2_(out) wavefront, further wherein a resultant output wavefront obtainedfrom the interference of the M1 _(out) wavefront and the M2 _(out)wavefront is different than the input optical wavefront by an amountαH(x,y) where −π≦α≦π. According to an aspect, the device effects awavefront coding on the input wavefront expressed ase^(iαH(x,y))=(1−H)+e^(iα)H, wherein 1−H(x,y) is the half-tone phasecoding provided by the ON/OFF state of M1, H is the half-tone phasecoding provided by the OFF/ON state of M2, and e^(iα) represents therelative phase term between M1 _(out) and M2 _(out).

According to an aspect of the above described embodiments, a telecentrictelescope may be disposed in the output wavefront plane to shift theoutput plane further downstream. The size of the telescope aperture canbe used to control the size (X×Y) of the mirror sub-array over which thespatial averaging is performed in order to realize the half-toningeffects.

Another embodiment of the invention is directed to a method forcontrolling an optical wavefront WF, comprising the steps of providing afirst controllable binary MEMS device M1 ₁ comprising an (n_(x,y),m_(x,y))_(M1) mirror array, wherein each mirror can be set only to abinary ON/OFF position, and a second controllable binary MEMS device M2₁ comprising an (n_(x,y), m_(x,y))_(M2) mirror array, wherein eachmirror can be set only to a binary ON/OFF position; providing anincident optical wavefront WF_(1i); splitting the incident opticalwavefront into WF1 ₁ along a first optical path L1 ₁ to M1 ₁ and intoWF2 ₁ along a second optical path L2 ₁ to M2 ₁; modulating WF1 ₁reflected from M1 ₁ by setting at least one M1 mirror sub array(X_(x,y)×Y_(x,y))_(M1)<array (n_(x,y)×m_(x,y))_(M1) to an ON positionand modulating WF2 ₁ reflected from M2 ₁ by setting a complementary atleast one mirror sub array (X_(x,y)×Y_(x,y))_(M2)<array(n_(x,y)×m_(x,y))_(M2) to an OFF position; providing an optical pathlength difference ΔL1L2 in a range 0<ΔL1L2<(2n+1)λ/2, where n=0, 1, 3, .. . , so as to provide a phase shift≦π; and obtaining a desired outputoptical wavefront WF_(1o) by optically combining reflected WF1 ₁ andreflected WF2 ₁. According to an aspect, modulating a phase profile ofthe wavefront by setting the at least one mirror sub array(X_(x,y)×Y_(x,y)) to a selected ON/OFF position comprises providing anaveraged grey-scale pixel value over the sub array. An aspect furtherincludes employing a half-toning algorithm, wherein a single grey-scalepixel is represented by a spatially averaged dot pattern over the X×Ymirror sub array. As will be appreciated, the mirror sub array isequivalent to a mirror cluster that is used to define a pixel, as isknown in the field of digital imaging.

In various aspects of the above mentioned embodiments, the at least someof the mirror array is one or more cluster arrays X×Y (<n×m), whereineach mirror cluster array X×Y represents a pixel and is characterized byat least a two-level phase half-toning approximation. In particularaspects, X=Y and n=m.

These and other objects, advantages and benefits provided by embodimentsof the invention will now be set forth in detail with reference to thedetailed description and the drawing figures and as defined in theappended claims.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 shows a general Argand diagram, which is used to illustrate thegeometric representation of a complex number as simply a point in thecomplex plane, provided as an aid in understanding the invention;

FIGS. 2 a, 2 b and 2 c, respectively, illustrate a square wave patternused to modulate an input wavefront; an optical control componentaccording to an embodiment of the invention; and an Argand diagramrepresentation of the interferometric output from the optical controlcomponent;

FIGS. 3 a, 3 b and 3 c show alternating dark/bright bar patternsillustrating half-toning in conjunction with the component in FIG. 2 b.FIG. 3 a illustrates a cosine function; FIG. 3 b shows ahard-thresholding version of FIG. 3 a; and FIG. 3 c shows a half-tonedversion of FIG. 3 a obtained using the known Stucki algorithm;

FIG. 4 a shows an interferometer-based optical control device forgenerating an arbitrary wavefront a(x,y)exp[iθ(x,y)] according to anembodiment of the invention;

FIG. 4 b schematically illustrates a pixel point P(x,y) in an exemplary5×5 mirror sub array of the MEMS device of FIG. 4 a;

FIG. 4 c shows an Argand diagram representation of point P(x,y) of FIG.4 b;

FIG. 5 shows an interferometer-based optical control device forgenerating a selected wavefront exp[iθ(x,y)] according to anotherembodiment of the invention;

FIGS. 6 a-6 c show alternating dark/bright ring patterns illustratinghalf-toning in conjunction with the device in FIG. 5. FIG. 6 aillustrates a continuous quadratic phase function; FIG. 6 b shows ahard-thresholding version of FIG. 6 a; and FIG. 6 c shows a half-tonedversion of FIG. 6 a obtained using the known Stucki algorithm;

FIG. 7A shows a diffraction-interferometer-based optical control devicethat uses a two-level algorithm for generating a wavefront exp[iθ(x,y)]according to another embodiment of the invention;

FIG. 7B shows a diffraction-interferometer-based optical control devicethat uses a three level algorithm for generating an arbitrary wavefronta(x,y)exp[iθ(x,y)] according to another embodiment of the invention;

FIG. 8 is a schematic system diagram used to illustrate the concept ofpolarization controlled wavefront phase coding;

FIGS. 9 a and 9 b illustrate an exemplarypolarization-interference-based optical control device for generating anarbitrary wavefront, and the polarization states in different pixelblocks at an output screen of the device, respectively, according toanother embodiment of the invention; and

FIG. 10 schematically shows a telecentric telescope according to anaspect of the invention.

DETAILED DESCRIPTION OF A PREFERRED EMBODIMENT OF THE INVENTION

As used herein, the term ‘digital binary MEMS’ refers to amicro-electromechanical minor array system that is subject only tobinary (i.e., ON/OFF or 1,0) control by tilting each minor facet to aretro-reflecting (1) position for incident light (ON position) or to anoff-axis (0; tilted or OFF) reflecting position for the incident light.

The term ‘amplitude’ as used herein will be recognized by those skilledin the art as referring to a complex number with a real part and animaginary part or, equivalently, with an absolute value amplitude and aphase angle, as is a well-known signal representation in the solutionsof Maxwell's equations in a harmonic time-dependent formalism.

According to a first illustrative embodiment and with reference to FIGS.2 a-2 c and 3 a-3 c, we disclose a novel approach to wavefrontgeneration using binary amplitude modulation of an input plane wave. Thebasic problem of wavefront generation is to achieve a wavefrontdescribed by exp[iθ(x,y)], when the function θ(x,y) is specified. Usingthe relationexp[iθ(x,y)]=cos[θ(x,y)]+e ^(iπ/2) sin[θ(x,y)],   (1)we require a way to represent cos[θ(x,y)] and sin[θ(x,y)], which canthen be added interferometrically with the appropriate relative phaseterm of e^(iπ/2) to generate the desired wavefront. The cosine and sinecan take values in the range of [−1, 1].

A first embodiment according to the invention illustrates the generationof square-wave functions 120 that can take on bi-level values (+1,−1)using binary mirror (digital binary MEMS) devices. FIG. 2 a shows asquare-wave pattern 120 that may be used to modulate an input wavefront105 (FIG. 2 b). The square-wave function can take only two values: (+1),i.e., e^(iθ) corresponding to a phase of θ=0 and (−1), i.e., e^(iθ)corresponding to a phase of θ=π radians. FIG. 2 b shows a firstinterferometrically-based optical control component 100 for obtainingthe square-wave modulation 120 of the input plane wave 105. The inputwavefront 105 is split into two equal (non-complex) amplitude parts by afirst component beam divider/combiner 102 that is disposed along a firstcomponent optical path 103 of the incident wavefront. The reflectedsplit wavefront is incident on a first component digital binary MEMSdevice M1 ₁. M1 ₁ comprises a mirror array 107 denoted by(n_(x,y)×m_(x,y))_(M1). The M1 ₁ optical path 109 from the beam splittersurface to M1 ₁ and back to the beam splitter surface (i.e., doublepass) has an optical path length L1 ₁. The transmitted split wavefrontis incident on a first component digital binary MEMS device M2 ₁. M2 ₁comprises a mirror array 111 denoted by (n_(x,y)×m_(x,y))_(M2). In anexemplary aspect, n=m. The M2 ₁ optical path 113 from the beam splittersurface to M2 ₁ and back to the beam splitter surface has an opticalpath length L2 ₁. Phase retarder means 115, in the form of a phaseplate, differential optical path length or other known phase alteringcomponent or technique for producing a differential optical path ΔL1L2equal to λ/2 (λ/4 per pass) is also shown. In the MEMS array M1 ₁, a subarray X×Y (<n×m) of minors corresponding to a (+1) value (θ=0) of thesquare-wave are ON, whereas in the MEMS array M2 ₁, a complementary subarray of minors X×Y corresponding to a (−1) value (θ=π) of the squarewave are ON. In an exemplary aspect, X=Y. A phase difference of πradians between the two reflected wavefront components is introducedusing an extra optical path difference ΔL1L2 equal to λ/2 in the M2 ₁optical path, which is achieved as shown in FIG. 2 b by translating M2 ₁by λ/4 relative to M1 ₁. However, in order to generate either cosine orsine functions as discussed above, one must be able to representgrey-scale values in terms of two levels: (+1) and (−1). This can beachieved by averaging over the sub arrays of the two levels (+1) and(−1) using a half-toning technique as described below.

Half-toning algorithms are widely used in printing devices where it isrequired to represent grey-scale pictures using only two levels; i.e., ablack dot or a blank white space. According to the embodiment, a singlegrey-scale pixel in a half-toned picture consists of a dot pattern overan exemplary block (X×Y) of 3×3 or 5×5 mirrors. The grey-scale isachieved using spatial averaging over this block. Both the filling-in ofthe outputs of the binary mirror (0,1) and the grey-levels areaccomplished simply by light propagation. The diffraction spreadingdistance λR/w equal to 2w, in order to have a spreading into e.g., 9mirror segments (3×3) is easily computed, where λ is the wavelength, Ris the distance and w is the pixel size. For w=10 μm and λ=0.5 μm, R=400μm. This distance is sufficiently small so that the filling-in of thewavefront is not a problem in a practical device. When a half-tonedpattern is printed on a paper and viewed by an observer, the spatialaveraging is performed by the human eye. The eye, however, cannotresolve the fine dot pattern, so the printed image appears to haveseveral levels between the black dot and the white blank.

FIGS. 3 a-3 c show alternating bar pattern illustrations of half-toningfor a cosine function between two levels (+1) and (−1). The opticalcontrol component 100 in FIG. 2 b functions as an interferometer forgenerating a wavefront with two phase levels. The component 100 MEMSarrays M1 ₁, M2 ₁ can be controlled so that the mirror sub arrays withlevels (+1) and (−1) are arranged according to a selected half-toningalgorithm. FIG. 3 a shows a cosine function. FIG. 3 b shows ahard-thresholded version of the cosine function; i.e., the non-negativepixels in FIG. 3 a are assigned a value of (+1), whereas the negativepixels are assigned a value of (−1). It can be seen that the grey-scaleis completely lost in this simple thresholding operation. FIG. 3 c showsa half-toned version of the cosine function using the well known Stuckihalf-toning algorithm. The grey-scale effect is now achieved by usingspatial averaging over a block of 10 pixels implying that 11 grey-levels(0-10) are achievable in a spatial-averaged sense. The white and blackpixels in FIG. 3 c represent values of (+1) and (−1) respectively. Thehalf-toning concept can thus be used for generating the sine and cosinefunctions for an arbitrary wavefront. The inventors are not aware of theprior use of the half-toning concept in the context of wavefrontgeneration as further described below.

Using the optical control component 100 shown in FIG. 2 b, one canobtain a half-toned version of the sine or cosine functions required forwavefront generation. The (+1) and (−1) minor sub arrays (pixels) in thehalf-toned pattern are turned ON in MEMS arrays M1 ₁ and M2 ₁,respectively. The value (−1) is achieved from the path difference of λ/2in the two arms of the component. Spatial averaging over pixel blocks isachieved simply by propagating the light over a very short distance. Fora given θ(x,y), it is thus possible to generate cos[θ(x,y)] andsin[θ(x,y)] by using a control component 100 as shown in FIG. 2 b.

FIG. 4 a shows an interferometer-based optical control device 300. Thedevice 300 comprises two identical components 100 (200) as shown in FIG.2 b for generating a wavefront described by exp[iθ(x,y)]. An incomingwavefront 106 is split into two output optical wavefronts 105 by aninput beam divider 302 (e.g., an X-cube). The two output opticalwavefronts 105 are the input optical wavefronts to the device components100, 200. One arm of the device 300 consists of a first optical controlcomponent 100 as described above. Control component 100 provides anoutput 120 in the form cos[θ(x,y)]. A second arm of device 300 consistsof a second optical control component 200 that is essentially identicalto component 100. Component 200 includes a second component beamdivider/combiner 202 disposed along a second component input opticalpath 203 of an input optical wavefront 105. A second component digitalbinary MEMS device M1 ₂ comprising an n×m mirror array 207 denoted by(n_(x,y), m_(x,y))_(M1) is disposed optically downstream of the secondbeam divider/combiner component 202 along an M1 ₂ optical path 213having a total optical path length L1 ₂. A second component digitalbinary MEMS device M2 ₂ comprising an n×m mirror array 211 denoted by(n_(x,y), m_(x,y))_(M2) is disposed optically downstream of the secondbeam divider/combiner component 202 along an M2 ₂ optical path 214having a total optical path length L2 ₂ that is different than the M1 ₂optical path 213. Phase retarder means 215 are employed to make L1 ₂different than L2 ₂. At least some sub array (X×Y) of the mirror array207 is in an ON/OFF state and a complementary at least some similar subarray of the mirror array 211 is in an OFF/ON state. As such, component200 functions similarly to component 100 but produces an output 220 inthe form sin[θ(x,y)]. An output beam combiner 318 is disposed in outputoptical paths 117, 217 to optically combine the respective cos[θ(x,y)]and sin[θ(x,y)] modulated outputs. Phase shifting means 322 disposedbetween beam splitter 202 and output beam combiner 318 provides a phasedifference equal to π/2. The resultant output wavefront 325 expressed ase^(iθ(x,y)) thus has a different phase than the input optical wavefrontby an amount θ(x,y).

FIG. 4 b illustrates a pixel P(x,y) in an exemplary 5×5 mirror sub array(X×Y) of a MEMS component of FIG. 4 a. At point P(x,y), the complexamplitude at point P has the form e^(iθ(x,y)) consisting of a realnumber (amplitude) part (cos θ) and an imaginary (phase) part i(sin θ)making up the complex amplitude value. FIG. 4 c is an Argand diagramrepresentation of the complex amplitude at P(x,y) where thecircumference of the circle is the locus of amplitudes and phase atposition P. In the example, the real amplitude value is one.

The interferometer device 300 illustrated in FIG. 4( a) may also be usedto generate a complex optical wavefront having a varying absolute valueof amplitude denoted by a(x,y). More precisely, the use of half-toningconcepts on the sub-assemblies 100, 200 allows one to use component 100for the generation of a(x,y)cos θ(x,y) and, similarly, component 200 forthe generation of a(x,y)sin θ(x,y), where 0≦a(x,y)≦1. An output functiong(x,y) can thus be obtained by combining the two outputs as follows:g(x,y)=a(x,y)exp[iθ(x,y)]=a(x,y)[cos θ(x,y)+i sin θ(x,y)].Hence, the wavefront generation device can be used to generate anoptical wavefront of arbitrary absolute value amplitude and phase.

Another embodiment of the invention is directed to a device andassociated method for more advanced wavefront coding, benefiting from asimplification of hardware used in the embodiment described abovethrough the employment of a more sophisticated algorithm. According tothis embodiment, one may again generate a phase function θ(x,y),0≦θ(x,y)≦α, for a constant angle α, using only binary (0,1) typeamplitude modulation. Thus we intend to generate an output wavefrontexpressed as e^(iθ(x,y)). As a first step, we convert θ(x,y) to a binarypicture H(x,y), which is a two-dimensional array with either zeros orones. Therefore, we let θ(x,y)≈αH(x,y) so that e^(iθ(x,y)) can beexpressed as e^(iαH(x,y)). The exponential can be expressed in thewell-known form as:e ^(iαH(x,y))=1+iαH+[(iα)²/2!]H ²+ . . .   (2)For i H(x,y) values limited to (0,1), H ^(N) =H; thus   (3)

$\begin{matrix}\begin{matrix}{{\mathbb{e}}^{{\mathbb{i}}\;\alpha\;{H{({x,y})}}} = {\left\lbrack {1 - {\left( {\alpha^{2}/{2!}} \right)H} + {\left( {\alpha^{4}/{4!}} \right)H} - \ldots}\mspace{14mu} \right\rbrack +}} \\{{\mathbb{i}}\;{H\left\lbrack {\alpha - \left( {\alpha^{3}/{3!}} \right) + \left( {\alpha^{5}/{5!}} \right) - \ldots}\mspace{14mu} \right\rbrack}} \\{= {\left( {1 - H} \right) + {H\left\lbrack {1 - \left( {\alpha^{2}/{2!}} \right) + \left( {\alpha^{4}/{4!}} \right) - \ldots}\mspace{14mu} \right\rbrack} + (5)}} \\{{\mathbb{i}}\;{H\left\lbrack {\alpha - \left( {\alpha^{3}/{3!}} \right) + \left( {\alpha^{5}/{5!}} \right) - \ldots}\mspace{14mu} \right\rbrack}} \\{= {\left( {1 - H} \right) + {{H\left\lbrack {{\cos\;\alpha} + {{\mathbb{i}}\;\sin\;\alpha}} \right\rbrack}(6)}}} \\{= {\left( {1 - H} \right) + {H\;{\exp\left( {{\mathbb{i}}\;\alpha} \right)}(7)}}}\end{matrix} & (4)\end{matrix}$The novel algorithm leading to equation (7) may be realized in atwo-beam interferometer device. Table II shows the values taken by thetwo terms in right hand side of equation (7) for the two values (0,1)taken by H.

TABLE II (1 − H) H exp(iα) H = 0 1 0 H = 1 0 exp(iα)Thus if H=0, then e^(iαH)=1 and the corresponding pixel phase is zero;and if H=1, then e^(iαH)=e^(iα) and the corresponding pixel phase is α,where H represents a half-tone phase value obtained by turning a MEMS₁sub array X×Y ON, and (1−H) represents the complement of H obtained byturning a MEMS₂ sub array X×Y OFF. By propagation or low-pass filtering,as is well-known to an optical engineer, one obtains an output that isan average over a block of m×m pixels. It is thus possible to obtain m²(e.g., 3×3 or 5×5) levels of phase between 0 to α.

The results of the novel two-level algorithm presented above may berealized by the optical control device 400 illustrated in FIG. 5. Thedevice 400 comprises a beam divider/combiner 402 disposed along an inputoptical path 403 of an incident optical wavefront 405. Incidentwavefront 405 may be a plane wave expressed as e^(iθ(x,y)) or anaberrated wavefront expressed as e^(−iφ(x,y)). A first digital binaryMEMS device M1 comprises an n×m mirror array (n_(x,y), m_(x,y))_(M1) 407disposed optically downstream of the first component beamdivider/combiner along an M1 optical path 409. At least some sub array(X×Y)_(M1) of the mirror array is programmed to be in an ON/OFF statethat provides a half-tone phase value expressed as 1−H(x,y), whereinH(x,y) represents a two-level value equal to 0 or 1 as described above.A second digital binary MEMS device M2 has an n×m mirror array (n_(x,y),m_(x,y))_(M2) 411 disposed optically downstream of the beamdivider/combiner along an M2 optical path 413. A complementary mirrorsub array (X×Y)_(M2) is programmed to be in an OFF/ON state thatprovides a half-tone phase value expressed as H(x,y) as shown in FIG. 5.Phase retarder means 415 are provided to obtain a controlled phasedifference between the M1 _(out) wavefront and the M2 _(out) wavefrontof α/2. A resultant output wavefront 421 expressed as e^(iαH) obtainedfrom the interference of the M1 _(out) wavefront (1−H) and the M2 _(out)wavefront (H). The wavefront 421 thus has a phase difference from theinput optical wavefront 405 by an amount αH(x,y) (equal to θ(x,y)),where −π≦α≦π. If the input wave is an aberrated wavefront expressed ase^(−iφ(x,y)) as referred to above, then the output wavefront from device400 will be expressed as e^(i[θ(x,y)−φ(x,y)]). The device operationchanges the phase between the optical input and optical output by θ(x,y)radians.

An exemplary illustration is shown in FIG. 6 a-6 c when H is a quadraticfunction (x²+y²) and the wavefront expression is exp[iα(x²+y²)]. FIG. 6a shows the profile of a continuous quadratic phase function. FIG. 6 bshows the phase profile obtained by hard-thresholding of the FIG. 6 aprofile at a level between 0 to 2π. FIG. 6 c shows the half-tonedversion of the FIG. 6 a profile using the Stucki algorithm. In thefigure, a white dot denotes phase=0; a black dot denotes phase=πradians. Grayscale effect is achieved in the half-toned FIG. 6 c bymeans of spatial averaging.

FIG. 7A illustrates an embodiment of a wavefront control device 600-1that uses a two-level half-toning algorithm for controlled wavefrontgeneration. Apart from adaptive optics applications, the inventors haverecognized a need for a spatial phase modulation that is independent ofwavelength. Potential applications may include various defense-based andspace-borne interferometer systems. For example, one may need a phasefront of θ(x,y) in the blue wavelengths (λ₁) and thereafter wish togenerate the same phase θ(x,y) in the red portion (λ₂) of the spectrum.An interferometer-based optical control device 600-1 that supports thiscapability uses a modified form of an achromatic phase-shiftinginterferometer. In this regard, the disclosure of U.S. Pat. No.4,786,124 is herein incorporated by reference in its entirety to thefullest allowable extent. Device 600-1 includes a diffractive, inputwavefront divider/combiner 602 denoted by G1 disposed along an opticalaxis 603 of an input wavefront 601. A first component diffractivewavefront divider/combiner 607 denoted by G2 is disposed to opticallyintercept a positive 609 (or a negative 611) n^(th)-order output beamfrom the input wavefront divider/combiner 602. In an exemplary aspect, afirst-order diffractive beam from G1 is incident on G2 (and as describedbelow, a negative first-order diffractive beam from G1 is incident onG3). A first component digital binary MEMS device 612 denoted by M1 isdisposed optically downstream of the first beam divider/combinercomponent along an M1 optical path 615 providing an optical path length(double pass) of L2. M1 comprises an n×m mirror array (n_(x,y),m_(x,y))_(M1) 613 (not shown). The mirror array includes a mirror subarray (X×Y<n×m) that is in a selected complimentary ON/OFF state thatprovides a two-level half-tone phase value (1−H(x,y)), where 0≦(1−H)≦1(e.g., H=0,1). According to an illustrative aspect, H(x,y) has thevalues (0,1). A second component digital binary MEMS device 622 denotedby M2 is disposed optically downstream of the second beamdivider/combiner component along an M2 optical path 625 providing anoptical path length (double pass) of L3. M2 comprises an n×m mirrorarray (n_(x,y), m_(x,y))_(M2) 623 (not shown). The mirror array includesa mirror sub array (X×Y<n×m) that is in a selected complementary OFF/ONstate that provides a two-level half-tone phase value (1−H(x,y)), where0≦(1−H)≦1 (e.g., H=0,1). Optical component 630 is provided to in-couplethe input wavefront 601 and out-couple the resultant output wavefront645. In a particular aspect, G1, G2 and G3 are diffraction gratings eachhaving a grating period Λ. G2 is displaced transversely a distances drelative to G3, where 0<d<Λ, to provide a phase shift α/2 between thetwo arms of the device. For achromatic operation, L2 is equal to L3. Thedevice 600-1 provides a resultant output wavefront 645 expressed ase^(iαH(x,y)) with a controlled phase αH(x,y) that is different than theinput wavefront phase. The device 600-1 and operation thereof may havefurther potential application for phase correction in sparse-aperturetelescope systems.

FIG. 7B illustrates another embodiment of a wavefront control device600-2, similar to control device 600-1, that uses a three-levelhalf-toning algorithm for controlled, arbitrary wavefront generation.The inventors recognize the need for a wavefront control device that cangenerate an arbitrary wavefront a(x,y) exp[iθ(x,y)]. A wavefront controldevice 600-2 as illustrated in FIG. 7B is based on a novel algorithmthat provides a three-level interferometric binary structure derived asfollows. It is possible to write identities for expressing phase interms of amplitude modulation when more than two levels are used toobtain θ(x,y) values spanning the whole complex plane. For example, fora three-level algorithm in which each pixel in H(x,y) can take threevalues, e.g., (0, ½, 1), the wavefront can be represented as follows:exp[iαH(x,y)]=[1−3H+2H ²]+4[H−H ²]exp(iα/2)+[−H+2H ²]exp(iα).   (8)It is thus possible to express phase as a sum of polynomials in H(x,y)with appropriate phase. Table III shows the values taken by the threeterms on the right hand side of equation (8) for the three values (0,½, 1) taken by H.

TABLE III 1 − 3H + 4 [H − [−H + 2H² H²] exp(iα/2) 2H²] exp(iα) H = 0 1 00 H = ½ 0 exp(iα/2) 0 H = 1 0 0 exp(iα)This algorithm can be embodied by the grating-based interferometerdevice 600-2 illustrated in FIG. 7A. The device will be capable ofgenerating an arbitrary wavefront a(x,y) exp[iθ(x,y)] using all-digitalbinary MEMS as disclosed herein. As shown, the input beam 601 is splitby grating 602 (denoted by G1) into three beams: a zero-order beam 635and ±1^(st)-order beams 609, 611. The three beams 635, 611 and 609 haverespective two-way or total phase delays of 0, α/2 and α. Asillustrated, the path lengths of the three beams have been made balancedor of equal length. The reflected beams from the new MEMS 640 (denotednow by M1) and MEMS 612 (M2) and 622 (M3) are combined at grating 602(G1) and directed by the beam splitter 630 to provide an arbitrarywavefront a(x,y) exp[iθ(x,y)]. As described herein, appropriatehalf-toning techniques are used to generate the required absoluteamplitude a(x,y).

Another embodiment of the invention directed to a polarization-basedoptical control device and method will now be described in relation toFIGS. 8, 9 a and 9 b. The current embodiment allows output wavefrontphase control through polarization modulation of the incoming wavefront.An explanation of the meaning of phase difference between two beams indifferent states of polarization will aid in illustrating the exemplaryembodiment presented below.

With reference to the illustrative system 800 in FIG. 8, consider anincoming plane polarized beam 805 having polarization axes x, y as shownsplit in two parts L1, L2 by a beam-splitter 802. The two beams L1, L2pass through respective birefringent media 807, 817 (e.g., a series ofquarter or half-wave plates) having some relative orientationdifference, which are located in plane I. The two beams acquire distinctstates of elliptical polarization expressed as E₁=a₁x+b₁e^(iφ1) andE₂=a₂x+b₂e^(iφ2)y at observation plane II. It can be assumed that thetwo beams gain the same phase due solely to their propagation. However,the two beams have a relative phase difference between them from thechange in polarization state. A simple criterion for the phasedifference between two beams in two different polarization states is asfollows: if the two beams in distinct polarization states described byvectors E₁ and E₂ are interfered, the resultant intensity is given by:I ₁₂ =|E ₁|² +|E ₂|²+2|E ₁ ∥E ₂|cos φ₁₂   (8)The phase between the two polarization states is φ₁₂ as seen from thecross-term. According to the instant embodiment, half-toning algorithmscan be employed to generate variable polarization states across thetransverse cross section of the wavefront.

An exemplary case is illustrated with reference to optical controldevice 900 in FIG. 9 a. An incident plane wave P(x,y) 905 polarized at45° is split into two polarization states P1, P2 by a polarizing beamsplitter 902 disposed along optical axis 903. A first digital binaryMEMS device 910 denoted by M1 is disposed optically downstream of thepolarizing beam splitter 902 along an M1 optical path 909. M1 comprisesan n×m mirror array (n_(x,y), m_(x,y))_(M1) 907 in which a mirror subarray X×Y (<n×m) is in a selected ON/OFF state that provides P1 with ahalf-tone phase value represented as (1−H), where 0≦(1−H)≦1. A seconddigital binary MEMS device 912 denoted by M2 is disposed opticallydownstream of the polarizing beam splitter 902 along an M2 optical path913. M2 comprises an n×m mirror array (n_(x,y), m_(x,y))_(M2) 911, inwhich a complementary mirror sub array X×Y (<n×m) is in a selectedcomplementary OFF/ON state that provides P2 with a half-tone phase valueH, where 0≦H≦1. The reflected wavefronts P1, P2, each having passedtwice through a quarter wave plate so as to couple efficiently throughthe beam combiner/divider, are optically combined by the polarizing beamsplitter 902 to produce a resultant output wavefront 920 propagatingalong an output optical wavefront path 917.

FIG. 9 b illustrates the polarization states 950 in two representativeindividual pixel blocks 960, 965 corresponding to two illustrative 2×2mirror sub arrays 970, 975. The two orthogonal polarization states x, ywill not exhibit any interference as the corresponding cross-term inequation (7) would be zero. However, averaging over the pixel blocks960, 965 gives rise to a gray-scale in polarization state. For example,block 960 can be characterized by E₁=2x+2y; block 965 can becharacterized by E₂=3x+1y. Pixels in the averaged or low-pass filteredwavefront thus have a polarization state in between two orthogonalstates used for half-toning. In FIG. 9 b, the two pixel blocks can thusacquire a phase difference φ₁₂ as given in equation (8), which can beused for phase correction in adaptive imaging applications. While asimple illustration of two orthogonally polarized components without anyadditional phase terms has been presented, a person skilled in the artwill appreciate that more general realizations involving two ellipticalpolarization levels for half-toning are also possible. Moreover, aperson skilled in the art will recognize that this embodiment, which hasbeen described for the generation of the wavefront exp[iθ(x,y)], may beemployed to generate an arbitrary wavefront a(x,y)exp[iθ(x,y)] byappropriate algorithmic control of the half-toning process as describedabove.

The embodiments described above disclose various digital binary MEMSmirror array configurations for phase front coding. The device andmethod embodiments have current and prospective widespread applicabilityto various adaptive optical systems, including, for example, those usedin defense related atmospheric compensation and in laser fusion.

FIG. 10 depicts the use of a telecentric telescope 1000 with anillustrative digital binary MEMS device 1010 according to an embodimentof the invention. As shown in the figure, an output wavefront 1020 isgenerated in plane I by the device 1010. If desired, the output planecan be optically shifted downstream to plane III. This may be achievedby inserting the telecentric telescope 1000 between planes I and III asshown. The size D of the aperture 1030 in plane II controls the size(X×Y) of the mirror sub-array over which the spatial averaging isperformed in order to realize the desired half-toning effects describedabove.

Having thus described the various embodiments of the invention, it willbe apparent to those skilled in the art that the foregoing detaileddisclosure is presented by way of example only and thus is not limiting.Various alterations, improvements and modifications recognized by thoseskilled in the art, though not expressly stated herein, may be made andare intended to be within the spirit and scope of the claimed invention.Additionally, the recited order of processing elements or sequences, orthe use of numbers, letters, or other designations, is not intended tolimit the claimed processes to any order except as may be specified inthe claims. Accordingly, embodiments of the invention are limited onlyby the following claims and equivalents thereto.

REFERENCES

The subject matter disclosed in the following citations is hereinincorporated by reference in their entireties to the fullest extentallowed by applicable laws and rules.

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1. An optical control device, comprising: a first optical controlcomponent, comprising a first component beam divider/combiner disposedalong a first component input optical path of an incident opticalwavefront; a first component binary MEMS device M1 ₁comprising an(n_(x,y)×m_(x,y))_(M1) mirror array disposed optically downstream of thecomponent beam divided/combiner along an M1 optical path having a totaloptical path lengh L1 ₁; a first component binary MEMS device M2 ₁comprising an (n_(x,y)×m_(x,y))_(M2) mirror array disposed opticallydownstream of the first component beam divided/combiner along an M2 ₁optical path different than the M1 ₁ optical path having a total opticalpath length L2 ₁; and phase retarder means for making L1 ₁ differentthan L2 ₁; wherein an at least one M1 ₁ sub array (X×Y)_(M1) is in anON/OFF state and a complementary an at least one M2 ₁ sub array(X×Y)_(M2) is in an OFF/ON state, further wherein an output wavefrontpropagating along a first component output optical wavefront path has acontrolled modulation, further wherein L1 ₁ is different than L2 ₁ by anamount Δ₁ L1 L2, where 0<Δ₁L1 L2<(2n+1)λ/2, where n=0, 1, 3, . . . so asto provide a phase shift<π radians; a second optical control component,comprising: a second component beam divider/combiner disposed along asecond component input optical path of an input optical wavefront; asecond component binary MEMS device M1 ₂ comprising an (n_(x,y)×m_(x,y))_(M1) mirror array disposed optically downstream of the secondbeam divider/combiner component along an M1 ₂ optical path having atotal optical path length L1 ₂; a second component binary MEMS device M2₂ comprising an (n_(x,y)x m_(x,y))_(M2) minor array disposed opticallydownstream of the second beam divider/combiner component along an M2 ₂optical path different than the M1 ₂ optical path having a total opticalpath length L2 ₂; and phase retarder means for making L1 ₂ differentthan L2 ₂, wherein an at least one M1 ₂ sub array (X×Y)_(M2) is in anON/OFF state and a complementary an at least one M2 ₂ sub array(X×Y)_(M2) is in an OFF/ON state, further wherein an output wavefrontpropagating along a second component output optical wavefront path has acontrolled modulation; an input beam divider disposed opticallyintermediate an incoming wavefront and the first and second opticalcontrol components, wherein the output optical wavefront from the inputbeam divider is the input optical wavefront to the first and secondoptical control components; an output beam combiner disposed tooptically combine the respective first and second component modulatedoutput wavefronts; and phase shifting means for providing a controlledphase difference between the first and second component phase modulatedoutput wavefronts, wherein a resultant output wavefront has a differentphase than the input optical wavefront by an amount θ(x,y).
 2. Thedevice of claim 1, wherein L1 ₂ is different than L2 ₂ by an amountΔ₂L1L2 where 0 <Δ₂L1L2 ≦(2n+1)λ/2, where n =0, 1, 3, . . . , so as toprovide a phase shift≦π radians.
 3. The device of claim 1, wherein X =Yand n =m.
 4. The device of claim 1, wherein the M1 ₂ sub array(X×Y)_(M1) in an ON/OFF state and the complementary M2 ₂ sub array(X×Y)_(M2) in the OFF/ON state are each one or more cluster arrays X×Y<n×m, further wherein each cluster array X×Y is characterized by atleast a two level half-toning phase approximation.
 5. The device ofclaim 1, wherein the device is a phase screen.
 6. The device of claim 1,further comprising an optical telescope disposed optically downstream ofthe output wavefront of the device.
 7. The device of claim 6, whereinthe telescope is a telecentric configuration that has an aperture thatcontrols the mirror sub array size.
 8. An optical control device,comprising: a first diffractive, input wavefront divider/combiner (G1)disposed along an optical axis of an input wavefront; a first componentdiffractive wavefront divider/combiner (G2) disposed to opticallyintercept one of a positive and a negative n^(th)−order output beam fromthe input wavefront divider/combiner; a first component binary MEMSdevice M1 comprising an (n_(x,y)×m_(x,y))_(M1) mirror array disposedoptically downstream of the first beam divider/combiner component alongan M1 optical path, wherein an at least one mirror sub array (X×Y)_(M1)is in a selected ON/OFF state that provides a two level half-tone phasevalue expressed as H(x,y), where 0 ≦H≦1; a second component diffractivewavefront divider/combiner (G3) disposed to optically intercept one of acomplementary negative and a positive n^(th)-order output beam from theinput wavefront divider/combiner; a second component binary MEMS deviceM2 comprising an (n_(x,y)×m_(x,y))_(M2) mirror array disposed opticallydownstream of the second beam divider/combiner component along an M2optical path, wherein an at least one minor sub array (X×Y)_(M2) is in aselected complementary OFF/ON state that provides a two-level half-tonephase value expressed as (1−H(x,y)), where 0 ≦(1−H) ≦1; and at least oneoptical component that in-couples the input wavefront and out-couples anoutput wavefront having a controlled phase that is different than theinput wavefront phase.
 9. The device of claim 8, wherein the firstdiffractive wavefront divider/combiner, the first component diffractivewavefront divider/combiner and the second component diffractivewavefront divider/combiner are diffraction gratings each having agrating period Λ.
 10. The device of claim 9, wherein G2 and G3 aredisposed in a common plane and one of G2 and G3 is transverselydisplaced relative to the other with respect to its respectiven^(th)-order output beam by a distance d, where 0 <d <Λ.
 11. The deviceof claim 10, wherein d =λ/ 2 for a π radian phase shift.
 12. The deviceof claim 8, wherein the positive and negative n^(th)-order output beamsare n equal to ±1 order.
 13. The device of claim 8, whereinH(x,y)=(0,1).
 14. The device of claim 8, wherein the device is a phasescreen.
 15. The device of claim 8, further comprising an opticaltelescope disposed Optically downstream of the output wavefront of thedevice.
 16. The device of claim 15, wherein the telescope is atelecentric configuration that has an aperture that controls the mirrorsub array size.
 17. An optical control device, comprising: a firstdiffractive, input wavefront divider/combiner (G1) disposed along anoptical axis of an input wavefront; a first component binary MEMS deviceM1 comprising an (n_(x,y)×m_(x,y))_(M1) mirror array disposed along anM1 optical path to intercept a zero-order output beam from the inputwavefront divider/combiner, wherein an at least one mirror sub array(X×Y)_(M1) is in a selected ON/OFF state that provides a three levelhalf-tone phase value expressed in terms of H(x,y), where H(x,y)=(0, ½,1); a first component diffractive wavefront divider/combiner (G2)disposed to optically intercept one of a positive and a negativen^(th)-order output beam from the first input wavefrontdivider/combiner; a second component binary MEMS device M2 comprising an(n_(x,y)×m_(x,y))_(M2) minor array disposed optically downstream of thefirst beam divider/combiner component along an M2 optical path, whereinan at least one mirror sub array (X×Y)_(M2) is in a selected ON/OFFstate that provides a three-level half-tone phase value expressed interms of H(x,y), where H(x,y)=(0, ½, 1); a second component diffractivewavefront divider/combiner (G3) disposed to optically intercept one of acomplementary negative and a positive n^(th)-order output beam from thefirst input wavefront divider/combiner; a second component binary MEMSdevice M3 comprising an (n_(x,y)×m_(x,y))_(M3) minor array disposedoptically downstream of the second beam divider/combiner component alongan M3 optical path, wherein an at least one mirror sub array (X×Y)_(M3)is in a selected OFF/ON state that provides a three-level half-tonephase value expressed in terms of H(x,y), where H(x,y)=(0, ½, 1); and atleast one optical component that in-couples the input wavefront andout-couples an output wavefront having a controlled, arbitrary phasethat is different than the input wavefront phase.
 18. The device ofclaim 17, wherein the first diffractive wavefront divider/combiner (G1),the first component diffractive wavefront divider/combiner (G2) and thesecond component diffractive wavefront divider/combiner (G3) arediffraction gratings each having a grating period Λ.
 19. The device ofclaim 18, wherein G2 and G3 are disposed in a common plane and G2 and G3are respectively transversely displaced by a distance, d₂, d₃, relativeto G1, where 0<(d₂,d₃,)<Λ.
 20. The device of claim 19, wherein d₂provides a total phase delay of α/2 and d₃ provides a total phase delayof α.
 21. The device of claim 17, wherein M1 has a half-tone phase valueexpressed as 1−3H+2H²; M2 has a half-tone phase value expressed as4(H−H²); M3 has a half-tone phase value expressed as (−H+2H²); and anoutput wavefront is expressed ase^(iαH(x,y))=[1−3H+2H²]+4(H−H²)e(^(iα/2))+(−H+2H²)e^(iα).
 22. An opticalcontrol device, comprising: a polarizing beam divider/combiner disposedalong a component input optical path of an incident optical wavefront,providing one polarization state P1 ₁ and another polarization state P2₁; a first binary MEMS device M1 ₁ comprising an (n_(x,y)×m_(x,y))_(M1)mirror array disposed optically downstream of the polarizing beamdivider/combiner along an M1 ₁ optical path of P1 ₁, wherein an at leastone mirror sub array (X×Y)_(M1) is in a selected ON/OFF state thatprovides a half-tone phase value (1−H), where 0≦(1−H)≦1; a second binaryMEMS device M2 ₁ comprising an (n_(x,y), m_(x,y))_(M2) mirror arraydisposed optically downstream of the polarizing beam divider/combineralong an M2 ₁ optical path of P2 ₁, wherein an at least one mirror subarray (X×Y)_(M2) is in a selected complementary OFF/ON state thatprovides a half-tone phase value H, where 0≦H≦1, further wherein anoutput wavefront propagating along an output optical wavefront path hasa polarization coded phase profile over a transverse cross section ofthe output wavefront.
 23. The device of claim 22, further comprising anoptical telescope disposed optically downstream of the output wavefrontof the device.
 24. The device of claim 23, wherein the telescope is atelecentric configuration that has an aperture that controls the mirrorsub array size.
 25. An optical control device, comprising: a beamdivider/combiner disposed along an input optical path of an incidentoptical wavefront; a first binary MEMS device M1 comprising an(n_(x,y)×m_(x,y))_(M1) mirror array disposed optically downstream of thefirst component beam divider/combiner along an M1 optical path providingan M1 _(out) wavefront, wherein an at least one mirror sub array(X×Y)_(M1) is in an ON/OFF state that provides a half-tone phase valueexpressed as (1−H(x,y)), wherein H(x,y) represents a two-level valueequal to 0 or 1; a second binary MEMS device M2 comprising an(n_(x,y)×m_(x,y))_(M2) mirror array disposed optically downstream of thebeam divider/combiner along an M2 optical path providing an M2 _(out)wavefront, wherein a complementary an at least one mirror sub array(X×Y)_(M2) is in an OFF/ON state that provides a half-tone phase valueexpressed as H(x,y); and phase retarder means for providing a controlledphase difference between the M1 _(out) wavefront and the M2 _(out)wavefront, further wherein a resultant output wavefront obtained fromthe interference of the M1 _(out) wavefront and the M1 _(out) wavefronthas a phase that is different than the input optical wavefront phase byan amount αH(x,y) where −π≦α≦π radians.
 26. The device of claim 25,wherein the device effects a wavefront coding on the input wavefrontexpressed as e^(iαH(x,y))=(1−H)+e^(iα)H, wherein (1−H(x,y)) is ahalf-tone phase coding provided by the ON/OFF state of M1, H is ahalf-tone phase coding provided by the OFF/ON state of M2, and e^(iα)represents the phase retardation between M1 _(out) and M2 _(out). 27.The device of claim 25, further comprising an optical telescope disposedoptically downstream of the output wavefront of the device.
 28. Thedevice of claim 27, wherein the telescope is a telecentric configurationthat has an aperture that controls the mirror sub array size.
 29. Amethod for generating a controlled output wavefront from a given inputwavefront, comprising the steps of: providing an interferometerincluding a plurality of controllable binary MEMS devices M(n) eachincluding an (n×m)_(M(n)) mirror array, wherein each array mirror can beset only to a binary ON/OFF position; controlling at least one sub array(X×Y)_(M(n))<(n×m)_(M(n)) of each mirror array according to an at leasttwo-level half-toning algorithm describing a phase value denoted by ahalf-toned picture H(x,y) where H(x,y) is a two-dimensional array;providing an optical phase delay between at least two of the pluralityof beams corresponding to the plurality of binary MEMS devices; andoptically combining the plurality of beams to generate the controlledoutput wavefront.
 30. The method according to claim 29, wherein thecontrolled output wavefront has the form e^(iθ(x,y)), further wherein(n)=2, comprising configuring the at least one sub array (X×Y)_(M(1)) ofM(1) in the form (1−H(x,y)) and the at least one sub array (X×Y)_(M(2))of M(2) in the form H(x,y) where H(x,y) can only have the values (0,1).31. The method according to claim 29, wherein the controlled outputwavefront has the form e^(iθ(x,y)), further wherein (n)=2, comprisingconfiguring the at least one sub array (X×Y)_(M(1)) of M(1) in the formH(x,y) and the at least one sub array (X×Y)_(M(2)) of M(2) in the form(1−H(x,y)), where H(x,y) can only have the values (0,1).
 32. The methodaccording to claim 29, wherein the controlled output wavefront has theform e^(iθ(x,y)), further wherein (n)=2, comprising configuring the atleast one sub array (X×Y)_(M(1)) of M(1) in the form (1−H(x,y)) and theat least one sub array (X×Y)_(M(2)) of M(2) in the form H(x,y), whereH(x,y) can only have the values (0,1).
 33. The method according to claim29, wherein the controlled output wavefront has the form e^(iθ(x,y)),further wherein (n)=3, comprising configuring the at least one sub array(X×Y)_(M(1)) of M(1) in the form [1−3H(x,y)+2H(x,y)²], the at least onesub array (X×Y)_(M(2)) of M(2) in the form [4(H(x,y)−H(x,y)²)], and theat least one sub array (X×Y)_(M(3)) of M(3) in the form[−H(x,y)+2H(x,y)², where H(x,y) can only have the values (0,½,1). 34.The method according to claim 33, comprising generating a controlled,arbitrary output wavefront of the form a(x,y)e^(iθ(x,y)).